A method for accelerating identification of sensitivity analysis of parameters, space and physical fields in a multi-field coupling system based on deep learning
By accelerating the identification of parameters and spatial sensitivity in multi-field coupled systems through deep learning, the limitations of traditional methods in terms of efficiency and accuracy are overcome, and efficient and accurate analysis and decision support for multi-field coupled systems are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2025-06-11
- Publication Date
- 2026-07-07
Smart Images
Figure CN120671245B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of underground engineering resource development and utilization, and particularly relates to a sensitivity analysis method for identifying parameters, spatial and physical fields in multi-field coupled systems based on deep learning. Background Technology
[0002] In underground space and resource development, THMC (temperature-flow-stress-chemical) multi-field coupling phenomena are prevalent. Accurately understanding and mastering these multi-field coupling processes is crucial for optimizing resource extraction, assessing environmental risks, and ensuring long-term engineering safety in fields such as geothermal energy development, carbon dioxide geological storage, and underground nuclear waste disposal. However, multi-field coupling processes exhibit strong nonlinearity and complex multiphysics interdependence, posing numerous challenges to existing models in handling these issues. On the one hand, models struggle to fully capture the complexities of the real world, often requiring simplification, which introduces uncertainty and reduces prediction accuracy. On the other hand, uncertainties in model parameters, such as measurement errors, scale effects, and unclear parameter relationships, further exacerbate the modeling difficulty. To address these issues, sensitivity analysis becomes a key tool, identifying critical sources of model uncertainty and providing direction for model improvement and system regulation. Traditional methods have limitations in performing sensitivity analysis, such as: experimental methods offer high accuracy but are expensive; mechanistic modeling is computationally complex and neglects higher-order coupling effects; and traditional machine learning is insufficient in capturing nonlinear relationships. Monte Carlo-based sampling uncertainty analysis plays a crucial role in characterizing and quantifying uncertainty and is considered the most reliable technique. As an emerging prediction technique, deep learning can effectively capture the nonlinear relationships in data and construct high-precision, highly generalizable regression prediction models. Therefore, utilizing deep learning to accelerate the prediction and convergence process of Monte Carlo global sensitivity analysis is of great significance for quantifying the uncertainty of complex multi-field coupled processes. Summary of the Invention
[0003] To address the aforementioned technical problems, this invention proposes a sensitivity analysis method based on deep learning to accelerate the identification of parameters, spatial and physical fields in multi-field coupled systems. This method can quickly and efficiently identify key parameters, physical fields and spatial regions, providing support for underground engineering decision-making.
[0004] To achieve the above objectives, this invention provides a method for accelerating the identification of sensitivity analysis of parameters, spatial and physical fields in multi-field coupled systems based on deep learning, comprising:
[0005] Constructing a multi-field coupled numerical model: Establishing a field-scale multi-physics coupled model based on geological data;
[0006] Training dataset generation based on Monte Carlo simulation: Multiple sets of parameter instances are generated through Latin hypercube sampling, numerical simulation is performed, and the output results are stored.
[0007] Training deep learning agent models: Employing an improved ResNet-18 architecture with R... 2 RMSE is used as an indicator to optimize model parameters and establish a regression mapping between parameters and output;
[0008] Analyze the three levels of sensitivity: calculate the global average first-order Sobol exponent to quantify parameter sensitivity; accumulate the contribution values of physical field parameters to distinguish the dominant physical field and formulate decoupling strategies; draw a spatial sensitivity distribution map to optimize the monitoring network layout.
[0009] Optionally, the multi-field coupling model is based on TOUGHREACT-FLAC. 3D The software is built and the parameters are calibrated based on the geological and statistical characteristics of the target reservoir.
[0010] Optionally, the deep learning agent model comprises four stages and six residual units, capturing spatial heterogeneity through convolutional layers.
[0011] Optionally, the decoupling strategy includes: simplifying the CO2-fluid response to a seepage-stress coupling model; and using a seepage-stress-chemical coupling model for the mineral reaction.
[0012] Optionally, the optimized monitoring network layout includes: optimizing the layout of monitoring points based on spatial sensitivity distribution.
[0013] Optionally, the deep learning model training includes: determining the coefficients R... 2 The optimization targets are >0.98 and root mean square error (RMSE).
[0014] An electronic device, characterized in that the device comprises: a processor and a memory storing computer program instructions; the processor, when executing the computer program instructions, implements the aforementioned sensitivity analysis method for recognizing parameters, space, and physical fields in a multi-field coupled system based on deep learning.
[0015] A computer storage medium, characterized in that the computer storage medium stores computer program instructions, which, when executed by a processor, implement the aforementioned sensitivity analysis method for identifying parameters, space, and physical fields in a multi-field coupled system based on deep learning.
[0016] Technical Effects of this Invention: This invention discloses a sensitivity analysis method for identifying parameters, spatial and physical fields in multi-field coupled systems based on deep learning. By constructing an integrated analysis framework based on deep learning, it significantly improves the efficiency and accuracy of uncertainty quantification in multi-field coupled systems and provides clear decision-making basis for engineering optimization. Firstly, addressing the pain point of long computation time in traditional numerical models, this invention uses a deep learning surrogate model with an improved ResNet-18 framework to replace the traditional numerical model in the sensitivity analysis based on Monte Carlo simulation, improving computational efficiency by four orders of magnitude. Simultaneously, it maintains the deterministic coefficient R0. 2 With a sensitivity index >0.98, this invention effectively captures higher-order coupling effects between parameters and nonlinear mappings from parameters to responses. Furthermore, this invention innovatively proposes a three-level sensitivity analysis system: quantifying parameter sensitivity through a global average first-order Sobol exponent to identify key parameters such as injection flow rate and fracture spacing; decoupling multi-field coupling mechanisms through the cumulative contribution value of the physical field, simplifying the full coupling to a seepage-stress coupling model for CO2-fluid responses and employing a seepage-stress-chemical coupling model for mineral reactions, avoiding error accumulation caused by traditional simplification methods; and finally, optimizing the monitoring network layout through spatial sensitivity distribution maps, such as deploying pressure sensors near production wells based on sensitive area identification in supercritical carbon dioxide geothermal systems. This invention achieves end-to-end optimization from efficient computation to accurate decision-making, providing a standardized solution for the safe control of multi-field coupled systems in underground engineering. Attached Figure Description
[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:
[0018] Figure 1 This is a flowchart illustrating a method for sensitivity analysis of parameters, space, and physical fields in a multi-field coupled system based on deep learning, according to an embodiment of the present invention.
[0019] Figure 2 This is a scatter plot comparing the Min-Max normalized results of multi-field coupled numerical simulation and alternative model predictions in an embodiment of the present invention.
[0020] Figure 3 This is a schematic diagram of the Sobol exponents of the first three parameters of all response variables in an embodiment of the present invention;
[0021] Figure 4 This is a schematic diagram of the first-order Sobol exponent (S1) distribution of the first three contributing parameters of CO2(aq) concentration in an embodiment of the present invention. Detailed Implementation
[0022] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0023] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0024] Existing solutions include:
[0025] Experimental method: This method directly measures the influence of multi-field coupled model parameters (such as porosity, adsorption coefficient, and displacement pressure) on the system response (such as porosity and permeability) through physical experiments (e.g., core displacement). The data is reliable and highly accurate, suitable for small-scale mechanism verification. However, it is expensive, time-consuming, and difficult to reproduce complex subsurface conditions (such as heterogeneity and multi-field coupling). In multi-field coupled systems, it is often used to calibrate mechanistic models or verify surrogate models, but it cannot cover the entire parameter space.
[0026] Mechanistic modeling: Based on physical equations and the general properties of rocks, a set of multi-field coupled equations is directly constructed and solved numerically. Its advantages lie in strong physical interpretability and support for long-term predictions (such as the millennium-long evolution of nuclear waste repositories). However, the computational cost is extremely high (a single simulation requires hours of CPU time), and higher-order coupling effects (such as chemomechanical feedback) are often simplified. Typical tools include TOUGHREACT-FLAC. 3D It is suitable for mechanism studies, but difficult to use for large-scale sensitivity analysis.
[0027] Traditional machine learning: Traditional machine learning (such as support vector machines and random forests) establishes a mapping relationship between parameters and responses through statistical learning. It is computationally efficient (predicting in seconds) and suitable for parameter selection (such as ranking geothermal sensitive parameters). However, it relies on a large amount of data, is insufficient in capturing high-dimensional nonlinear relationships, and has poor physical interpretability.
[0028] Computer-aided experimental design and analysis: This approach efficiently explores the parameter space through sampling designs (such as Latin hypercube sampling) and surrogate models (Kriging, PCE), combined with Sobol exponential quantification of sensitivity. It balances efficiency and accuracy, clearly separating main effects and interaction effects, and is suitable for mid-dimensional problems. However, it faces limitations such as the curse of high dimensionality (student size increases dramatically when parameter dimension > 20), insufficient nonlinearity capture, and difficulties in multi-field coupling analysis (requiring field-specific modeling).
[0029] The purpose of this invention is to provide an integrated framework that combines deep learning-based surrogate models with global sensitivity analysis to address the problems of low computational efficiency and poor accuracy in uncertainty quantification of multi-field coupled systems using existing technologies. This framework aims to efficiently analyze the sensitivity of model parameters, physical fields, and spatial domains, thereby identifying key parameters, optimizing system performance, and providing a more reliable basis for engineering design and decision-making.
[0030] like Figure 1 As shown, this embodiment provides a method for sensitivity analysis of parameters, space, and physical fields in a multi-field coupled system based on deep learning, including:
[0031] Constructing a multi-field coupled numerical model: Establishing a field-scale multi-physics coupled model based on geological data;
[0032] Training dataset generation based on Monte Carlo simulation: Multiple sets of parameter instances are generated through Latin hypercube sampling, numerical simulation is performed, and the output results are stored.
[0033] Training deep learning agent models: Employing an improved ResNet-18 architecture with R... 2 RMSE is used as an indicator to optimize model parameters and establish a regression mapping between parameters and output;
[0034] Analyze the three levels of sensitivity: calculate the global average first-order Sobol exponent to quantify parameter sensitivity; accumulate the contribution values of physical field parameters to distinguish the dominant physical field and formulate decoupling strategies; draw a spatial sensitivity distribution map to optimize the monitoring network layout.
[0035] Furthermore, the multi-field coupling model is based on TOUGHREACT-FLAC. 3D The software is built and the parameters are calibrated based on the geological and statistical characteristics of the target reservoir.
[0036] Furthermore, the deep learning agent model comprises four stages and six residual units, capturing spatial heterogeneity through convolutional layers.
[0037] Furthermore, the decoupling strategy includes: simplifying the CO2-fluid response to a seepage-stress coupling model; and adopting a seepage-stress-chemical coupling model for the mineral reaction.
[0038] Furthermore, the optimized monitoring network layout includes: optimizing the layout of monitoring points based on spatial sensitivity distribution.
[0039] Furthermore, the deep learning model training includes: determining the coefficients R... 2 The optimization targets are >0.98 and root mean square error (RMSE).
[0040] Specifically, such as Figure 1The implementation process of the present invention shown includes:
[0041] This invention employs a multi-field coupling model: based on geological and geophysical data of the study area, utilizing TOUGHREACT-FLAC... 3D The coupled framework constructs a numerical model of a supercritical carbon dioxide enhanced geothermal system (scCO2-EGS) at the field scale, or based on other sites or other software, only requiring the provision of a multi-field coupled forward model.
[0042] The training dataset of this invention consists of selected input parameters and prior intervals. Numerical simulations are performed based on Latin hypercube sampling (LHS) to generate multiple sets of samples as the data basis for subsequent alternative model construction.
[0043] This invention is based on a deep learning (DNN) surrogate model: a deep neural network surrogate model is constructed using an improved ResNet-18 architecture. This model comprises four stages and six residual units. Convolutional layers capture the impact of structural heterogeneity on the output response space characteristics, while residual units alleviate the vanishing and exploding gradient problems, accelerating model convergence. During training, model parameters are optimized by minimizing the regularized L1 norm loss function, enabling the model to accurately establish a regression mapping relationship between multi-field coupled model parameters and system output. Based on the research objectives and dataset characteristics, a suitable deep learning algorithm is selected and constructed. Preprocessed data is input into the model for training to determine the optimal parameter combination. The deterministic coefficients (R²) are then used to determine the optimal parameter combination. 2 The root mean square error (RMSE) and the root mean square error (RMSE) are used as evaluation metrics for model fit to ensure that the model's predictive performance supports the subsequent Monte Carlo sensitivity analysis.
[0044] The sensitivity analysis module of this invention performs Sobol sampling and uses a trained alternative model to predict the output of the sampled parameter set. It quantifies the direct contribution ranking of the response variable based on the average first-order Sobol exponent across the entire model domain; it determines the dominant physical field of the response quantity based on the cumulative contribution of all parameters in each physical field and customizes a decoupling scheme accordingly; it obtains more site information from the regional distribution of sensitivity and rationally sets up the monitoring network based on the spatial sensitivity differences of the grid.
[0045] Taking the simulation of a multi-field fully coupled supercritical carbon dioxide enhanced geothermal system as an example, this framework is used to conduct a multi-level global sensitivity analysis of the system. The implementation process is as follows:
[0046] (1) Data Collection and Model Building: A conceptual model of scCO2-EGS was designed based on the geological conditions and injection-production scheme of the study site. The TOUGHREACT-FLAC model was then used. 3DNumerical simulation software is used to establish a multi-field coupled model and determine the initial and boundary conditions of the model, such as formation temperature, injected fluid, and the locations of injection wells and production wells.
[0047] (2) Generation of the training dataset: 24 key parameters (injection flow rate, rock specific heat capacity, initial fracture aperture, etc.) and 14 response variables (CO2(aq) concentration, porosity, etc.) of the multi-field coupled model were determined, and prior distributions were assigned to the parameters. Subsequently, Latin hypercube sampling was used to generate 1000 parameter instances in the defined multi-dimensional parameter space. Then, each set of parameters was input into the multi-field coupled model, and ensemble simulations were performed using a high-performance computing cluster. The model output results were systematically stored. The 1000 samples were divided into training and test sets at a 9:1 ratio for the training and evaluation of subsequent alternative models.
[0048] (3) Alternative Model Construction and Training: First, the dataset was preprocessed, including logarithmic transformation and Min-Max normalization of the model's output response variables to avoid convergence difficulties caused by differences in the magnitude of parameters. Simultaneously, the parameters were decomposed into homogeneous and heterogeneous components based on their spatial distribution characteristics, mapped onto images, and concatenated into a 100×100 matrix for subsequent feature extraction. The ResNet-18 model was selected and improved for deep learning training on the preprocessed data. The coefficient of determination and root mean square error were used as evaluation metrics for model fit, acceptable hyperparameter combinations were determined, and a good regression mapping relationship was established between the parameters of the multi-field coupled model and the dynamic system output (such as permeability, porosity, solute concentration, and mineral volume fraction). Finally, the R-squared values of the alternative models corresponding to all response variables were obtained. 2 All indices are greater than 0.98, such as Figure 2 As shown.
[0049] (4) Global Sensitivity Analysis: Sensitivity analysis was performed using Sobol sampling (53,248 instances) to quantify the Sobol index of the 24 parameters controlling the multi-field coupled model on the output response of each grid in the scCO2-EGS model. During this process, an alternative model was used to efficiently predict the output. The sensitivity analysis consisted of three parts: (i) Parameter sensitivity analysis was quantified by computing the domain-averaged first-order Sobol index, which represents the average contribution of a single input parameter to the model output across all spatial grids, to identify key parameters that significantly influence the model output, such as... Figure 3As shown; (ii) the sensitivity contribution of each physical field to the model output is quantified by accumulating the S1 of all parameters in that field, so as to clarify the importance of different physical fields in the system, and accordingly simplify the coupling effect between physical fields; (iii) spatial sensitivity is characterized by plotting the spatially resolved S1, so as to intuitively show the spatial heterogeneity of the contribution of parameters to the model output within the simulation area, and provide a basis for optimizing the design of the monitoring network. Figure 4 As shown.
[0050] An electronic device, characterized in that the device comprises: a processor and a memory storing computer program instructions; the processor, when executing the computer program instructions, implements the aforementioned sensitivity analysis method for recognizing parameters, space, and physical fields in a multi-field coupled system based on deep learning.
[0051] A computer storage medium, characterized in that the computer storage medium stores computer program instructions, which, when executed by a processor, implement the aforementioned sensitivity analysis method for identifying parameters, space, and physical fields in a multi-field coupled system based on deep learning.
[0052] Alternative Option 1: In terms of constructing alternative models, other methods can be tried, such as multinomial models, radial basis functions (RBF), kriging models, DACE, etc.
[0053] Alternative Option 2: In terms of sensitivity analysis methods, other global sensitivity analysis methods can be considered to replace the Sobol index method, such as the Fourier Amplitude Sensitivity Test (FAST).
[0054] Alternative Option 3: In terms of sampling, for simpler models, orthogonal experimental design can be used to replace Latin hypercube sampling (LHS) to generate training datasets while ensuring accuracy. This can effectively reduce the number of samples and thus improve computational efficiency.
[0055] This invention is applicable to various underground engineering systems involving multi-field coupling processes, including but not limited to geothermal energy development, carbon dioxide geological storage, underground nuclear waste disposal, and groundwater resource management. It is used to analyze the impact of uncertainties in parameters, physical fields, and spatial domains on system performance and results.
[0056] This invention discloses a method for sensitivity analysis of parameters, space, and physical fields in multi-field coupled systems based on deep learning. By constructing an integrated analysis framework based on deep learning, it significantly improves the efficiency and accuracy of uncertainty quantification in multi-field coupled systems and provides clear decision-making basis for engineering optimization. First, addressing the pain point of long computation time of traditional numerical models, in the sensitivity analysis based on Monte Carlo simulation, this invention uses a deep learning surrogate model with an improved ResNet-18 framework to replace the traditional numerical model, improving computational efficiency by four orders of magnitude. Simultaneously, it ensures a deterministic coefficient R² > 0.98, effectively capturing higher-order coupling effects between parameters and nonlinear mappings from parameters to responses. Furthermore, this invention innovatively proposes a three-level sensitivity analysis system: First, it quantifies parameter sensitivity using the global average first-order Sobol exponent to identify key parameters such as injection flow rate and fracture spacing. Second, it decouples multi-field coupling mechanisms by using the cumulative contribution value of physical fields; for CO2-fluid response, the full coupling can be simplified to a seepage-stress coupling model, and for mineral reactions, a seepage-stress-chemical coupling model is adopted, avoiding error accumulation caused by traditional simplification methods. Finally, it optimizes the monitoring network layout through spatial sensitivity distribution maps; for example, in supercritical carbon dioxide geothermal systems, pressure sensors are deployed near production wells based on sensitive area identification. This technology achieves full-chain optimization from efficient calculation to accurate decision-making, providing a standardized solution for the safe control of multi-field coupling systems in underground engineering.
[0057] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for sensitivity analysis of parameters, spatial and physical fields in a multi-field coupled system based on deep learning, characterized in that, include: Constructing a multi-field coupled numerical model: Establishing a field-scale multi-physics coupled model based on geological data; Training dataset generation based on Monte Carlo simulation: Multiple sets of parameter instances are generated through Latin hypercube sampling, numerical simulation is performed, and the output results are stored. Training the deep learning surrogate model: An improved ResNet-18 architecture was used to optimize model parameters using R² and RMSE as metrics, and a regression mapping between parameters and output was established. A deep neural network surrogate model was constructed using the improved ResNet-18 architecture. This model contains 4 stages and 6 residual units. Convolutional layers capture the influence of structural heterogeneity on the output response space characteristics, and residual units alleviate the gradient vanishing and gradient exploding problems, accelerating model convergence. During training, the model parameters were optimized by minimizing the regularized L1 norm loss function, enabling the model to accurately establish the regression mapping relationship between multi-field coupled model parameters and system output. Based on the research objectives and dataset characteristics, a suitable deep learning algorithm was selected and constructed. The preprocessed data was input into the model for training to determine the optimal parameter combination. The coefficient of determination and root mean square error were used as evaluation metrics for model fit, ensuring that the model's prediction performance supports subsequent Monte Carlo sensitivity analysis. Analysis of Level 3 Sensitivity: Calculate the global average first-order Sobol exponent to quantify parameter sensitivity; Accumulate the contribution values of physical field parameters, distinguish the dominant physical field, and formulate a decoupling strategy; Draw a spatial sensitivity distribution map and optimize the monitoring network layout; The decoupling strategy includes: simplifying the CO2-fluid response to a seepage-stress coupling model; adopting a seepage-stress-chemical coupling model for mineral reactions; and optimizing the monitoring network layout by optimizing the layout of monitoring points based on spatial sensitivity distribution.
2. The sensitivity analysis method for parameters, space, and physical fields in a multi-field coupled system based on deep learning as described in claim 1, characterized in that, The multi-field coupling model is based on TOUGHREACT-FLAC. 3D The software is built and the parameters are calibrated based on the geological and statistical characteristics of the target reservoir.
3. The sensitivity analysis method for identifying parameters, spatial and physical fields in a multi-field coupled system based on deep learning as described in claim 1, characterized in that, The deep learning proxy model comprises four stages and six residual units, and captures spatial heterogeneity through convolutional layers.
4. The sensitivity analysis method for parameters, space, and physical fields in a multi-field coupled system based on deep learning as described in claim 1, characterized in that, The deep learning model training includes optimizing the deterministic coefficient R² > 0.98 and the root mean square error RMSE.
5. An electronic device, characterized in that, The device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the sensitivity analysis method for accelerating the identification of parameters, space and physical fields in a multi-field coupled system based on deep learning as described in any one of claims 1-4.
6. A computer storage medium, characterized in that, The computer storage medium stores computer program instructions, which, when executed by a processor, implement the sensitivity analysis method for accelerating the identification of parameters, space, and physical fields in a multi-field coupled system based on deep learning as described in any one of claims 1-4.